Marco's father had a mental breakdown when his wife died, and sank into a deep depression, even losing his job as a computer engineer. When he starts dating again, Marco doesn't really seem to have any problems with the new paramour herself; just her evil toy poodle, the fact that she's his math teacher (that'll teach Marco not to make the school call home!), and, oh, yeah—his mom's not really dead.
Unfortunately for the girlfriend (now his Dad's wife!), she ends up infested by the Yeerks after Marco tells his dad everything and finally rescues his mom.
Dexter: Dexter puts a great deal of time and effort into gaining the trust of girlfriend Rita's children. He does succeed and they get as attached to him as they're capable of. In the second novel, Dearly Devoted Dexter, we find out that Dexter and Cody have much more in common than one would want to think, given that Cody's eight. Astor seems to share her brother's issues, but is more inclined to spectate rather than participate. Dexter decides the kids need him to train them in the Code of Harry.
Anne Fine's Goggle-Eyes has the Tall, Dark, and Snarky Kitty Killin reminiscing about her antagonistic relationship with her mother's new boyfriend to a classmate with the same problem. The boyfriend is old enough to be her grandfather and disagrees with every political stance the family takes, but is supportive of it and is fatherly to Kitty's younger sister. Eventually, Kitty accepts him... right before her mother breaks it off.
I'm Ok (2018): Ok's mom is dating Deacon Koh from Ok's church. Ok doesn't like Deacon Koh because he thinks he's trying to hard to get Ok to like him back. His dislike only increases when he thinks he sees Deacon Koh stealing money from the church collection plate. Thankfully he gets over it, and he and Ok's mom get married near the end of the book.
The Princess Diaries has Mia's mom dating her algebra teacher, which freaks Mia out at first because while he's a nice enough guy, Mia struggles with the lesson itself. Eventually they marry and produce Mia's half-brother Rocky.
From Howl's Moving Castle, Sophie's father marries Fanny after the death of his first wife. However, she does treat her two stepdaughters and her own daughter fairly. But subtly, Martha points out that after their father's death, she had sent her two daughters away for her own reasons and had the eldest Sophie left with the family hat store without any pay.
In Half Magic by Edward Eager, the kids introduce their mother to the new paramour, and are mostly quite happy with the whole situation — except that they think it'd be strange to call him "father", so he gets declared an honorary uncle.
In later books of Percy Jackson and the Olympians, Percy's mother Sally begins dating Paul after her husband Gabe "mysteriously" disappears. Percy is fine with this for the most part (though he does call Paul "Blowfish" for some time after mishearing his last name) because Gabe was an abusive asshole to both him and Sally and Paul, in contrast, is a nice guy who makes Sally genuinely happy.
The titular character in Ella Enchanted isn't too happy when her father announces he's getting remarried after her mother's death. She's outright dismayed when she learns the woman he's marrying is the mother of her two worst enemies.
In The Changeover, right before Laura's little brother Jacko is attacked, their mother brings home her new paramour much to Laura's displeasure.
In Hamlet, this is one of the titular character's main sources of angst. Of course it doesn't help that the new paramour is his uncle. And technically usurped his right to the throne.
This happens in The Casual Vacancy to Gaia Bawden's mother, Kay, who moves both her and her daughter from London to the tiny village Pagford to be with her lover, Gavin. Gaia is not remotely happy about being uprooted from the place she grew up.
In The House of Night, Zoey's chief source of familial angst is the "Steploser", her ultra-religious stepfather who she feels stole her mother from her. Being Marked makes things worse between them, as he believes vampyres are satanic.
Miles: You don't need to bellow. Ivan: I'm not bellowing, I'm being firm! Miles: Could you please be firm at a lower volume? Ivan: No. Simon Illyan is sleeping with my mother, and it's your fault!
Gentleman Jole and the Red Queen: On the other hand, Miles himself takes Cordelia hooking up with admiral Jole after Aral's death much better, but then, as it turns out, Oliver Jole always was a third leg in their relationship, which he probably knew (or at least suspected) all along, so he had had time to get used to it.
Nina Tanleven: Nine doesnt react well to any woman who shows an interest in her father, feeling that he doesnt really notice if theyre interested and that this makes him an easy target for the kind of woman who would be willing to take advantage of him, and also because hes still married. While she does lighten up towards Mona Curtis in The Ghost Wore Gray and Norma Bliss in The Ghost in the Big Brass Bed, shes still not thrilled by their interest in her father.
In To All the Boys I've Loved Before, Lara Jean's father is dating Ms Rothchild. Each Song girl has a different reaction to it. Kitty is ecstatic as she is a Shipper on Deck for them from the beginning. Lara Jean is simply happy to see her father with someone. Margot on the other hand is more aloof to Ms Rothchild.